Preheat an outdoor grill for high heat. Lightly oil grill grate. Season chicken on both sides with steak seasoning. Grill 6 to 8 minutes on each side, until juices run clear. Cool and slice.
In a saucepan over low heat, mix the Alfredo sauce, bleu cheese dressing, and tomatoes. Cook and stir until the sauce boils.
Bring a large pot of lightly salted water to a boil. Add angel hair pasta, cook 2 to 4 minutes, until al dente, and drain. Transfer to a large bowl, and toss with the grilled chicken and sauce to serve.